Multiscale control concepts for transport-dominated problems

针对运输主导问题的多尺度控制概念

• 批准号: 423615040
• 负责人: Professorin Dr. Simone Göttlich
• 金额: --
• 依托单位: Lehrstuhl für wissenschaftliches Rechnen
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/423615040?language=en
• 关键词: Multiscale; control; concepts; transport; dominated

In recent years, the description of controllable (or active) particle systems using methods of kinetic gas theory has been achieved and allows now to tackle a wide range of applications as for example traffic flow. In this research project, the inherent hierarchy exploited extensively in kinetic theory for theoretical and numerical considerations will be investigated in order to develop novel analytical and numerical methods for control problems posed on multiple scales as well as under aspects of non-smoothness in the control.The work program includes the analysis of consistent optimality conditions within the model hierarchies, numerical analysis for control aspects relevant in particular on the highest level of the model hierarchy, as well as the development of numerical methods for time-dynamic non-smooth optimization problems on all levels. In addition to the sensitivity of non-smooth kinetic equations, the multi-scale nature of the equations raises questions for boundary control problems of nonlocal hyperbolic equations and switching systems.The participating project partners from Germany and South Africa have already cooperated in the past documented in joint work on hyperbolic equations, exchange programmes and jointly organized conferences.

近年来，已经实现了使用动力学气体理论的方法对可控（或主动）粒子系统的描述，并且现在允许处理广泛的应用，例如交通流。在本研究项目中，将对动力学理论中广泛用于理论和数值考虑的固有层次进行研究，以便为多尺度以及控制中的非光滑性方面提出的控制问题开发新的分析和数值方法。工作计划包括分析模型层次内的一致最优性条件，控制方面的数值分析，特别是在模型层次结构的最高级别，以及时间动态非光滑优化问题的数值方法的发展在所有级别上。除了非光滑动力学方程的敏感性之外，方程的多尺度性质还对非局部双曲方程和切换系统的边界控制问题提出了问题，来自德国和南非的参与项目伙伴过去已经在双曲方程、交流方案和联合组织会议的联合工作中进行了合作。